Getting instanced particles to follow paths of hairs in particle system with hair dynamics
You almost did it, just a few things to fix:

decimate the number of faces of the cylinder with the Decimate modifier, un-subdivide. The faces get multiplied by each particle. In Object mode, right-click the object and select Shade Smooth, and will look the same with only 300 vertices, that's 1/10th.

lay down the cylinder along the Y-axis by a -90° rotation around the X-axis in Object mode, apply the Rotation (Ctrl+A). Make sure that the cylinder's origin is at bottom of the mesh, at world origin. Apply Location if needed.

In Edit mode, move 3D Cursor to world origin (Shift+S), select all vertices (A), and select from menu: Mesh → Sort Elements... → Cursor Distance. This prevents strange things from happening as the particles bend and twist due to a change in wind direction.
layout of particle object

Change the settings of the Particle Instance modifier: (Pole Axis: Z, set Position: 1.000, clear Keep Shape checkbox)



Particles in the wind:

Blend file: